The objective of this study is to understand the flow above the front edge of low-rise building roofs. The greatest suction on the building is known to occur at this location as a result of the formation of conical vortices in the separated flow zone. It is expected that the relationship between this suction and upstream flow conditions can be better understood through the analysis of the vortex flow mechanism. Experimental measurements were used, along with predictions from numerical simulations of delta wing vortex flows, to develop a model of the pressure field within and beneath the conical vortex. The model accounts for the change in vortex suction with wind angle, and includes a parameter indicating the strength of the vortex. The model can be applied to both mean and time dependent surface pressures, and is validated in a companion paper.